> For the complete documentation index, see [llms.txt](https://torch-1.gitbook.io/litepaper/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://torch-1.gitbook.io/litepaper/payout-formula.md).

# Payout formula

If the actual price falls within the predicted range, the bet wins and is rewarded from the token's reserve using a computed multiplier, in addition to returning it. Core formula is

$$
\text{Payout} = \text{Base Payout} + \text{Reserve Bonus}
$$

**Base Payout** rewards the quality of the prediction based on how early, narrow, and bold it is. It reflects the bet’s accuracy and informational value.

**Reserve Bonus** is an additional reward drawn from surplus liquidity, shared proportionally among winning bets. It scales with stake size and only activates when the reserve is above a target threshold.

Let's look at each payout component in detail.

$$
\text{Base Payout} = \min(\text{Reserve Liquidity},  \text{Stake} + \text{Stake} \times \text{Prediction Quality})
$$

Where:

* Prediction Quality is a multiplier coefficient computed at betting time
* Reserve Liquidity is cap enforcement computed at resolution time

Prediction Quality components are

* Range [Sharpness](/litepaper/system-mechanics/sharpness-quality.md) = (High - Low) / Current Price
* [Boldness](/litepaper/system-mechanics/boldness-quality.md) = 1 - [Local Confidence](/litepaper/system-mechanics/local-confidence.md)
* [Lead Time](/litepaper/system-mechanics/lead-time-quality.md) = Resolution Time - Placement Time

The multiplier formula:

$$
\text{Prediction Quality} = \text{Scaling Factor} \times (\text{Lead Time Quality})^{w\_L} \times (\text{Boldness Quality})^{w\_B} \times (\text{Sharpness Quality})^{w\_S}
$$

Initial Monte Carlo simulation suggested Scaling Factor of 1 at project launch with the Weights set to 1/3. See quality calculations and their suggested launch configs in the ‘Key parameters’ section.

We use exponential weighting (i.e. raising each quality score to a weight) instead of additive weighting to compute overall Prediction Quality. This approach reflects the intuition that a strong prediction must balance timeliness, conviction, and precision, and excelling in one area cannot fully compensate for weakness in another.

Reserve Liquidity is simply its size that caps edge case payouts.

The payout system ensures that winning bets are fully covered by the token’s current reserve:

* At the moment of betting, the system checks whether a bet’s calculated payout based on its Prediction Quality score is fully covered by the reserve. If not, the bet is rejected.
* At the moment of resolution, the system checks whether a payout will drain the reserve in spite of its initially calculated safety. If so, it pays out as much as possible, waives the remainder, and attributes the difference to risk.

$$
\text{Reserve Bonus} = \text{Bonus Share}\times \text{Bonus Pool}
$$

Where:

* [Bonus Share](/litepaper/system-mechanics/bonus-share.md) is the share of the reserve bonus pool allocated to a winning bet
* [Bonus Pool](/litepaper/system-mechanics/bonus-pool.md) is the portion of the token’s reserve set aside for bonuses

Naturally, Reserve Bonus is capped by the available funds on top of Target Level.


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